BnB - tweaks for pseudosymmetry

Hi,

I’m using homogeneous and non uniform refinement at the moment on a pseudosymmetric assembly, and I’m wondering how the branch and bound algorithm used for these jobs copes with cases where there are multiple poses that are almost equivalent in terms of score, but very different in orientation.

Looking at Fig 3 of the original cryosparc paper, it seems like there is a possibility that for some particles the correct pose could be eliminated if the minima corresponding to the pseudosymmetrically related poses are close together in terms of score. Are there any parameters one can tweak to control how aggressively cryosparc prunes the search space at each iteration? So that one can search more comprehensively, at the expense of speed?

Cheers
Oli

My understanding is if there’s another minimum that juts down below the blue line in iteration 1 (top of part A), that part of the space is retained in iteration 2. It should keep the pseudosymmetric false minima across the iterations until the bound excludes them. Restated, eventually any non-marginalizing reconstruction will have to choose one alignment parameter; in cryoSPARC this should happen only after projection-matching against the current reconstruction gives error estimates that place the alternate parameters above the lower bound.

In a marginalizing program like Relion, you could instead end up with significant alignments at both minima and then have each particle inserted e.g. 40% at one and 60% at the other. Personally, I would rather have the single correct answer, but this approach can work well for some data (as we have no doubt all seen when using Relion).

The final option is something like pseudosymmetric refinement in Frealign (and the forthcoming cisTEM 2). There, the symmetry group is given with a lower-case code (“c4” instead of “C4”). Then the metadata file gets a line for each particle at each possible symmetry-related pose, each with its own occupancy and score. These scores are used for per-particle b-factor weighting, so particles can contribute low-frequency information to all symmetry-related poses and more high-frequency information just to the higher scoring one.

Assuming my understanding about cryoSPARC above is correct, then a possible tweak would be to always retain the poses which are symmetry-related to the best pose when computing the true error. This could go along well with limiting the search space for symmetric refinements, which cryoSPARC hasn’t done previously. It could then be requested using a checkbox for pseudosymmetric refinement, similar to giving a lower-case point group in Frealign.

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This would be great indeed. Also, I need to check out pseudosymmetric refinement in Frealign - I wasn’t aware of it, so thanks for the heads up!

Cheers
Oli

Hi @olibclarke @DanielAsarnow, this is indeed a very useful thread - thanks for the info!

@DanielAsarnow is correct that pseudosymmetry-related poses (that have similar residual error) should be retained until the latest iterations of BnB, especially since in cryoSPARC we don’t limit search to the asymmetric unit. But in practice due to the way poses are discretized for branching/bounding (and the interplay with discretized shifts), the pseudosymmetry-related poses may never be exactly compared and the correct one may get overlooked towards the end of BnB. e.g. consider a symmetry where the angle between asymmetrix units is not 90 degrees - this means already that the symmetry cannot be exactly represented on a cartesian grid.

I think marginalization (e.g. Relion) has a similar issue that the true pose will only end up with a larger weight if the fine-ness of sampling poses is high enough that a direct comparison is made between the pseudosymmetrically related poses. I’m not sure at what sampling level this would be fulfilled. The best approaches are definitely those that are specifically designed for pseudosymmetry. The suggestion @DanielAsarnow made for how to do this in cryoSPARC I think is the right direction. It’s on our list now :slight_smile:

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@olibclarke @apunjani thank you for bringing this important topic up. If you have a protein complex with 4 subunits, 3 of which are indentical, and the 4th is different from the other three by a disordered region which is not visible in the map, would it make sense to impose C4 symmetry or what artefacts could it bring ?